The assessment of thermoelastic attenuation is crucial in designing surface acoustic wave (SAW) devices. As irregular structures are more and more involved in modern applications for which efficient numerical tools are required, a multi-physics finite-element model is proposed in this paper, where thermoelastic damping in piezoelectric materials can be accounted for in both coated and uncoated conditions. The coupled equations are solved iteratively in time domain, using the Newmark method. The mechanical, electrical, and thermal degrees of freedom are calculated simultaneously at each time step. An application of the model is presented through the investigation of thermoelastic loss in a lithium niobate SAW device.